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Gough Stewart Platform


Gough Stewart Platform


I want to use a hexapod (gough stewart platform)  in mechanical application.

The hexapode is formed with:

_ 1 base plate (ground)

_ 1 end effector (platform)

_ 6 leg (mechanical drive effector)

This system have 6 DoF for platform

For build this mechanical device, I need to calculate:

_ inverse kinematics : If i know the posture of platform, I find the leg lenght

  (the posture is : 3 positions : dX,dY,dZ and 3 rotations : dRX,dRY,dRZ)

_ Leg Forces (traction-compression only generated in leg)

For start, i build the geometrical model, for this, i define a ground mark : O with coordinates 0,0,0


I define the hinge point of base : Ai


I define the hinge point of platform : Bi


I define the C point is the géometrical center of platform

Now the leg are AiBi vector


I define a user mark

The  user mark M ( 3 positions + 3 orientations) is define to mark O ( the origin of mark M is the point of interest)

For moving the platform, i define a new mark Mc from M

This mark is mark M augmented with strokes




And finally i calculate the AiBi vector, and i find the leg lenght.

I calculate AiBi at nominal position : not mouved platform

I calculate AiBi at mouved position

I find the stroke of effector (leg displacement)


Now I have a problem for Trajectory calculation

For know the stroke of effector, is necessary to compute leg lenght for trajectory.

The start point is define with stroke (in Mc)

dXmin  dRXmin

dYmin  dRYmin

dZmin dRZmin

The end point is

dXmax  dRXmax

dYmax  dRYmax

dZmax dRZmax

I use a lambda parameter for hash trajectory with 20 points for example

Now I find 20 group of position parameter.

I want to run my calculus for all position  group, and finally i make a graph with leg lenght for position parameter group.




My calculus is right for calculate leg lenght for one position of platforme in 3D space.

But i can’t calculate for trajectory ( group of parameter ) and i can’t make a graph

I’am a mechanical men, not a software programmer (lol)

Do you can to help me ?


Re: Gough Stewart Platform

and trajectory worksheet

Re: Gough Stewart Platform

in first step. Perhaps i make 2 program Smiley Frustrated



Calculate all coordinates for trajectory points in 3D space

with stroke data entrystroke.JPG




i make program wich calculate sucessive positions for all 6 parameters


example for only dX translation:

first position is  dXmin

second position is dXmin+dXstep

...  ( the step is (dXmax - dXmin) / lambda)

end with last position = dXmax


All position (dX,dY,dZ,dRX,dRY,dRZ) are must be concatenated in matrix Mc


Perhaps :program.JPG



Smiley Mad wrong ! it's don't work Smiley Sad

I am bad in programming  Smiley Sad

please help me

I don't understand to correctly use mathcad program Smiley Frustrated



Re: Gough Stewart Platform

It's good with LucMeekes solution (give me it in another post)Trajectory coordinates.JPG


i don't find it with program solutionsSmiley Sad

Re: Gough Stewart Platform

But i have problem with LucMeekes solution's


if the dY strokes = 0 (dYmin=0 , dYmax=0)

I don't have 0 in matrix ! because i divide by 0 in dY stroke calculus ! it,s wrong!

I want to give 0 in my matrix if  stroke =0

maybe it's necessary to build programming solution  for resolve this ?


i'm very sad, i'm alone in the dark with mathcad programming

Re: Gough Stewart Platform

And if i want calculate position for one point in 3D space ! it's same divide by 0


dxmax= 30

dxmin= 30

error !


Re: Gough Stewart Platform

I try it

example for stroke dX 0 to 5




but the first 0 is not correct Smiley Frustrated


I don't understand why i have this first 0 Smiley Sad

Re: Gough Stewart Platform

i find the problem

is ORIGIN Mathcad parameter Smiley Surprised



But it's not work correctlyprogram_2.JPG



and i need same number of point for each matrix



if dx have 20 rows

i need dy,dz,dRx,dRy,dRz have equal rows , here 20 rows

if, for example dy=0

i need 20 rows equal 0 in dy matrix ...

I'm very very bad in programming Smiley Mad


 And i need concatenated all in one matrix

Re: Gough Stewart Platform

I try itprogram 3.JPG



But i have another problem

it's OK for stroke = 0 at 0 positions


But it's wrong if the stroke =0 , nut the position = 5 for example

If dZmin= 5 and dZmax=5 the stroke =0 but the position of platform = 5

and finally i need my dZ matrix have :






for this last item, it's wrong, but i'm getting closer

Re: Gough Stewart Platform

You know the coordinates in 3D cartesean space of the base of your six effectors (the A's in your diagram.)  


If you know the posture of the platform then you know the coordinates of the B's, the ends of the effectors.


The length of each effector then is the magnitude of the vector |B-A|.


The challenge is going to be to restrict the platform to the range of acceptable effector lengths.